Computation of the magnetic potential induced by a collection of spherical particles using series expansions

In Magnetic Resonance Imaging there are several situations where, for simulation purposes, one wants to compute the magnetic field induced by a cluster of small metallic particles. Given the difficulty of the problem from a numerical point of view, the simplifying assumption that the field due to each particle interacts only with the main magnetic field but does not interact with the fields due to the other particles is usually made. In this paper we investigate from a mathematical point of view the relevancy of this assumption and provide error estimates for the scalar magnetic potential in terms of the key parameter that is the minimal distance between the particles. A special attention is paid to obtain explicit and relevant constants in the estimates. When the “non-interacting assumption” is deficient, we propose to compute a better approximation of the magnetic potential by taking into account pairwise magnetic field interactions between particles that enters in a general framework for computing the scalar magnetic potential as a series expansion.

The magnetic signatures of oceanic tides in satellite data: A virtual-observatory approach

<p>The magnetic signatures of the M<sub>2</sub>, and more recently also the N<sub>2</sub>, and O<sub>1</sub> oceanic tides have been successfully extracted from satellite observations (Grayver & Olsen, 2019). The traditional method uses the spatial representation of the tidal signals by spherical harmonics. Here we present an alternative approach based on the concept of virtual observatories, motivated by similar development in the analysis of the core field (Mandea & Olsen 2006). All quiet-time, night-side vector magnetic field values observed by the satellite(s) in the proximity of a selected virtual observatory are parameterized by a scalar magnetic potential represented by a cubic harmonic polynomial in a local Cartesian coordinate system. The time-dependence of the polynomial coefficients is constrained by selected tidal frequency, taking into account also the phase and amplitude corrections. The local approach offers several advantages over the use of the global spherical-harmonic base. The disturbances from external field in the polar areas have no impact on the inversion at lower latitudes, and local error estimates can be also provided. In this initial report, we will explore the possibilities of the new technique in terms of resolution, the combination of datasets from multiple satellites and the use of NS and EW field differences from the Swarm A-C pair.</p>

Analytical Solutions of Eddy-Current Problems in a Finite Length Cylinder

Magnetic field and eddy currents in a cylinder of finite length are calculated by separation of variables. The magnetic field outside the cylinder or inside the bore of the hollow cylinder and shell is expressed in terms of Bessel functions. Both axial and transverse applied fields are considered for the solid and hollow cylinders. The equations for the vector potential components are transformed in one-dimensional equations along the radial coordinate with the consequent integration by the method of variation of parameters. The equation for the scalar electric potential when required is also integrated analytically. Expressions for the magnetic moment and loss are derived. An alternative analytical solution in terms of scalar magnetic potential is derived for the finite length thin shells. All formulas are validated by the comparison with the solutions by finite–element and finite-difference methods.

Field – Circuit Model of Wireless Transmission Power System using Ω–T–T0 Formulation

The paper discusses the field-circuit model of the wireless power transmission system (WPTS) with the air-core high-frequency transformer. While working on the field model, a formulation which uses scalar magnetic potential Ω and electric vector potentials T and T0 was implemented. Model equations were provided. The system which consists of magnetically coupled coils connected with the elements of external circuits was taken into consideration. The selected results of simulation calculations were presented. The obtained results of simulation calculations were compared with the results of measurements obtained at a laboratory post.

Benchmark Solutions for Magnetic Fields in the Presence of Two Superconducting Spheres

A complete solution is presented for the boundary value problem of two perfect conductor spheres in a uniform magnetic field of arbitrary orientation. Expressions are given for the scalar magnetic potential and for the field intensity. They can readily be applied for calculating the forces between the spheres. Benchmark numerical results of specified accuracy are generated, which are also useful for validating various approximate numerical methods.

Numerical Study of Joint Magnetisztion and Gravitational Convection of Air in a Square Enclosure under Quadrupole Magnetic Field

Numerical computations were carried out for theromagnetic convection of air in a square enclosure under both magnetising and gravitational fields. Scalar magnetic potential method was used to calculate magnetic field. The governing equations in primitive variables were discretized by the finite-volume method and solved by the SIMPLE algorithm. The flow and temperature fields for the air natural convection were presented and the local and mean Nusselt numbers on the walls were calculated and compared. The results show that the magnetic force has significant effect on the flow field and heat transfer in a square enclosure, the average Nusselt number respects the trend of decrease first and then increase when the magnetic force number increases.

Edge pinch instability of oblate liquid metal drops in a transverse AC magnetic field

This paper considers the stability of liquid metal drops subject to a high-frequency AC magnetic field. An energy variation principle is derived in terms of the surface integral of the scalar magnetic potential. This principle is applied to a thin perfectly conducting liquid disk, which is used to model the drops constrained in a horizontal gap between two parallel insulating plates. Firstly, the stability of a circular disk is analysed with respect to small-amplitude harmonic edge perturbations. Analytical solution shows that the edge deformations with the azimuthal wavenumbers m = 2, 3, 4, . . . start to develop as the magnetic Bond number exceeds the critical threshold Bmc = 3π(m + 1)/2. The most unstable is m = 2 mode, which corresponds to an elliptical deformation. Secondly, strongly deformed equilibrium shapes are modelled numerically by minimising the associated energy in combination with the solution of a surface integral equation for the scalar magnetic potential on an unstructured triangular mesh. The edge instability is found to result in the equilibrium shapes of either two- or threefold rotational symmetry depending on the magnetic field strength and the initial perturbation. The shapes of higher rotational symmetries are unstable and fall back to one of these two basic states. The developed method is both efficient and accurate enough for modelling of strongly deformed drop shapes.